That depends on your license!
With a US CPL/IFR there is no chance in Europe, maybe @ freighter company's like FedEx or UPS, but their selection takes place in the US!
I got my German ATPL with minimum of 250hrs and i got hired. I only can speak for Germany but here you see quite often young men with 250 hrs entering an airliner cockpit. But currently we have more than 1000 unemployed young pilots here in Germany. The situation is really tough.
You definitely need a European license to find a job as a pilot with an European Airline.

HAHA...so you think you can get a job at a freighter company like UPS or Fedex with a CPL/IFR. Think again...1000 hours PIC turbine is one of the many requirements to get a job at UPS or Fedex. 250 hour pilots don't get jobs as airline pilots in the USA....and US certificated pilots don't get jobs in Europe unless they have the right to live and work there, and are certified under European pilot regulations.

what do I know!
there are some small freighter airlines who operate as FedEx feeders.
I never wrote an application to one if these companys, so i don't have any experience with them. Was just an idea!
But who flies the B727 based in CGN? Are that US crews on a 3 week trip in europe or are they fixed based here?

I have flown the 727's in CGN. We used to have layovers in OSL, CPH, and WAW....even before that some MAD and VIE. The trips are built for 12 days of work with a weekend layover in CGN. Crews are US based and either deadhead or commercial to CGN. I used to take LH a lot from YVR-FRA-CGN. Also, a European company called Star air does subcontracting for us on routes we can't fly do to political reasons. The only UPS crewed 727 left in Europe, now, is the WAW trip and it is VERY senior.

Speaking again only for germany or a part of europe I think until the hiring situation will become better we have to wait 4 years, maybe 5!
Here in Germany every year more than 1000people earn their ATPL and there are only 300-400 jobs available per year. So more than 60% will remain without a flightseat. That is a pretty sad sight seeing his collegues and friends writing more than 100 applications with no result. Only 3 of our course with 16 has benn hired untill now. I think that sais enough!
You can imagine how glad I am that i got a great job with a wonderful company!
Good lukc my friend I wish you all the best!